Standard Mandarin (Putonghua) is spoken by many people and in fact is the language with the most native speakers. There are then many people who acquire it as a second language increasing the number of speakers further. In a lot of places people will furthermore speak a local variant of Mandarin (e.g. in Sichuan). Both facts of Mandarin being learnt as a second language and spoken as in a variant form will definitely be a reason why "accented Mandarin" is an issue.

There is an easy way of expressing difference in pronunciation by using the Pinyin system. Though from a linguistic point of view this will probably not be very precise it should work for many cases. I thus want to give a list of possible variations on Mandarin by listing them using Pinyin initials and finals. The source used is:

Cornelius C. Kubler, George T.C. Ho: Varieties of Spoken Standard Chinese, Volume II: A Speaker from Taipei. Foris Publications, Dordrecht, 1984, ISBN 90-6765-040-4.

Initials:

• zh, ch, sh > z, c, s

  The retroflex initials will be pronounced as the alveolar equivalents, so 知道 zhīdao becomes zīdao.

• r > *z

  The retroflex r will sometimes be pronunced with, as the book states, similar to an English "z".

• f > h, hu

  According to the book both directions of change will occur: 政府 zhèngfǔ will become zènghǔ, 分化 fēnhuà becomes fēnfà.

• l, r > *r

  Both l and r are sometimes pronunced with a flapped r, according to the above source.

• n > l

  Confusion of n and l can happen, usually before nasal finals as in 南 nán which becomes lán.

• b, p, m, f, w +eng > b, p, m, f, w +ong

  Labial sounds ending with eng will change their final to ong, so 碰 pèng becomes *pòng.

Finals:

• ing, eng > in, en

  The velar nasal [ŋ] will be lost for ing, eng thus for 高兴 gāoxìng changing to gāoxìn.

• en > *En

  For final en the vowel originally pronounced in a mid central position will change to a mid front one, with no equivalence in the original Pinyin set.

• ü+ Ø, e, an, n > i+ Ø, e, an, n

  Vowel [y] (as in yu, nü, quan) will change to resemble the vowel denoted by i in Pinyin, as for 下雨 xià yǔ becoming xià yǐ.

• u+ o, ei > o, ei

  Diphthong uo and triphthong ui will degenerate as in 美国 měiguó with *měigó or 对 duì with dèi.

• zh, ch, sh, r, z, c, s +i > zh, ch, sh, r, z, c, s +u

  Vowel -i as for [z̩], [ʐ̩] will change to vowel u as for 知道 zhīdao with zūdao.

• e > o

  Final -e changes to -o, e.g. 可能 kěnéng to *kǒ'nén.

• r > Ø

  Erhua sound as in 画儿 huàr will mostly not be used.

Furthermore there are tonal changes, and hypercorrection is an issue, but for now I will finish.

Update: The greater sign doesn't necessarily indicate the direction of the change as hypercorrection will lead to changes backwards to the initial change and the given book doesn't always clearly state the major direction so that in at least on case the change pair was swapped here as to accommodate the given example.